The two ys must be the same. Equate the two right hand sides.
-x + 10 = x + 2 add x to both sides.
10 = x + x + 2
10 = 2x + 2 Subtract 2 from both sides.
8 = 2x Divide by 2
x = 8/2
x = 4
Now solve for y
y = x + 2
y = 4 + 2
y = 6
Use the other equation to check it.
y = - x + 10
y = -4 + 10
y = 6